The effect of temperature Huang-Rhys in the multiphonon non-radiative transitions

The calculated results of multiphonon non-radiative transitions probability factors I(ε) are presented by both of Huang Kun's statistical distribution theory of phonons and rigorous formula at finite temperature with six-frequency model. These results show that both of them are very consistent at weak coupling under any temperature. However, the remarkable deviation between statistical I(ε) and rigorous I(ε) will appear at strong coupling, high temperature. Moreover, the deviation will increase with the rising of temperature. In addition, the I(ε) is highly sensitive with the variation of Huang-Rhys factor. In particular, it has a region of maximum value for a proper coupling strength